Creating a spherical array
Add a sphere, copy it, scale it down in edit mode


Select the big sphere, go to the Object panel, under Duplication select Verts


Select the small sphere, hold shift, then select the big sphere. Hit CTRL+P and set the paren to Vertex


Result should look like that


You can now go select the big sphere again and go to edit mode, select all vertices. Use the "Randomize" option, I used a setting of 0.06.


You can use the Object info -> Random input together with a Math node to give them different colors.


This isn't an accurate representation of an atom I guess, but you said it's about simplicity and the visualisation aspect. 



P.S.: If you are worried about the top / bottom of the result, as there are more spheres, you can try another type of sphere for the big sphere, e.g. the icosphere, that has an even distribution of vertices.